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In Section 7.6 - Equivalence of Lagrange's and Newton's Equations in the Classical Dynamics of Particles and Systems book by Thornton and Marion, pages 255 and 256, introduces the following transformation from the x

My questions are mathematical rather than physical questions.

1. Could anyone please explain to me how did the Author make the derivative of x in Equation (7.100) and expanded the time derivative of x in the last term of Equation (7.108)?

2. Is there any mathematical relation of the partial derivatives used for the above two cases?

Your help is much appreciated. Thanks a lot...

_{i}-coordinates to the generalized coordinates q_{j}in Equation (7.99):My questions are mathematical rather than physical questions.

1. Could anyone please explain to me how did the Author make the derivative of x in Equation (7.100) and expanded the time derivative of x in the last term of Equation (7.108)?

2. Is there any mathematical relation of the partial derivatives used for the above two cases?

Your help is much appreciated. Thanks a lot...

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